We do know everything about the bitcoin client and protocol.
1. We don't know the private key to the Genesis Block.
2. We don't know, how x-value of half of the secp256k1 generator was picked.
3. We don't know, why some messages are in Big Endian, and others are in Little Endian (which is why you can skip some last rounds in SHA-256 computations, when checking if block hash has at least 32/64 leading zero bits).
And there are many more things we don't know.
I think that quote was referring to how and why bitcoin was created, rather than the technical code.
If you wonder "why", then the message in the Genesis Block is pretty clear. We had "second bailout", which was literally the input, which triggered making Bitcoin. And when it comes to "how", then note, that Proof of Work in hashcash just made the coins hard to get, and collecting every transaction by every P2P client is all you need, to mathematically solve the double spending problem.
And by extending that idea, you can easily solve the decentralized mining problem, if every P2P client will collect all blocks, produced by all miners. But we don't have enough resources, to really use that kind of model in practice, and make things tick with such N^2 complexity.
this would probably also infer the thorough doxing of satoshi
If everything would be revealed in a single shot, then maybe. But if things will be broken gradually, then it will hide him instead, by making it literally impossible for anyone to cryptographically prove, that a given person is Satoshi. If the key from the Genesis Block will be compromised, if the PGP key will be compromised, and if all other ways of sending "I am Satoshi" signal will be broken, then nobody would ever be able to reveal his identity, because all possible proofs will no longer be accepted by anyone.
What exactly you're talking about?
It is all about magic numbers. You can read the source code, which is responsible for computing SHA-256 hashes. But you don't know, why some magic numbers were picked the way they are. You can find some "nothing up my sleeve" numbers, for example when you try to square or cube some constants, but you don't know, why a given number of rotations was picked, why we have 64 rounds, why w-values can go back to their original values after certain number of rounds, and so on. There are many things we know, but there are also many things we don't know, and some of them are responsible for making things safe to use, as long as nobody knows it.
For example:
https://malicioussha1.github.io/If you change k-values into something unsafe, then your version of a given hash function is safe for users, but easy to break for the creator. And if there exist some reason, why k-values are square and cube roots, and you can use that property to mount a successful attack, then creators could potentially insert a backdoor, which would work only for them.
And the same is true for secp256k1: as long as computing n-value is fast, but breaking a private key is slow, then it works. But if there is any algorithm, which could take two public keys, and produce a distance between them, by making similar steps, as you have to make, when you compute n-value in Schoof-Elkies-Atkin algorithm, then it would be unsafe. And knowing "everything" would mean also knowing such shortcuts, which would make that kind of cryptography unsafe.
Because when we know everything about a given mathematical problem, then that system is fully broken, and we try to discover a new problem. And then, if it is unsolved for a long time, then humans can build a new system, which is safe, as long as a given math problem is unsolved. And the cryptography in practical use is just made out of unsolved math problems, there is nothing else than that.
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